Two events that are disjoint are not independent. This is because that disjoint events do not overlap, which means that if one event occurs, the other cannot. So, the occurrence of one event provides information about the absence of the other, which violates the definition of independence.
Two events A and B are considered independent if the occurrence of A has no effect on the likelihood of B occurring, and vice versa.
In other words, the probability of both events happening at the same time is equal to the product of their individual probabilities:
[tex]P(A and B) = P(A) * P(B) (B).[/tex]
This formula cannot be satisfied when two events are disjoint because if one event occurs, the other cannot occur. As a result, two disjoint events are not independent.
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kareem is trying to decide which college to attend full time next year. kareem believes there is a 55% chance that he will attend state college and a 33% chance that he will attend northern university. the probability that kareem will attend either state or northern is
Kareem's probability of attending either State or Northern is 0.88, meaning there is an 88% chance that Kareem will attend one of the universities.
Probability is a measure of the likelihood of an event occurring.
Kareem's case, the probability of attending State College is 55%, which means there is a 55% chance that Kareem will attend State College. The probability of attending Northern University is 33%, which means there is a 33% chance that Kareem will attend Northern University.
To determine the probability of attending either State or Northern, we add the individual probabilities of each event. Thus, the probability of attending either State or Northern is:
P(State) + P(Northern) = 0.55 + 0.33 = 0.88
The probability of attending either State or Northern is 0.88, which means there is an 88% chance that Kareem will attend one of these universities. It is important to note that the sum of all probabilities of all possible outcomes is always equal to 1.
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< A and < B are complementary angles.
Find the measure of
16
34
46
100
Step-by-step explanation:
Complementary angles add up to 90 degrees, so if one angle is known, the measure of its complement can be found by subtracting it from 90 degrees.
If <A is 16 degrees, then <B is 90 - 16 = 74 degrees.
If <A is 34 degrees, then <B is 90 - 34 = 56 degrees.
If <A is 46 degrees, then <B is 90 - 46 = 44 degrees.
If <A is 100 degrees, then <B is 90 - 100 = -10 degrees. However, angles can't be negative, so this solution is not valid.
carrie went running for 22 minutes and then did a series of exercises for 3 mins
Answer: Her total exercise time was 25 minutes
Write a rule for the n th term of the sequence for which a = 30 and r= 1/2
A rule for the nth term of the sequence for which a = 30 and r= 1/2 the 5th term of the sequence is 1.875.
What is the geometric sequence?
A geometric sequence is often referred to as geometric progression or geometric series is defined as a sequential pattern of non-zero numbers in which the following number's value is a multiplication from the preceding number by another constant non-zero number.
The rule for the nth term of a geometric sequence is given by the formula:
aₙ = a * r⁽ⁿ⁻¹⁾
where "a" is the first term in the sequence, "r" is the common ratio, and "n" is the position of the term in the sequence.
In this case, we have "a" = 30 and "r" = 1/2. Substituting these values into the formula, we get:
aₙ = 30 x (1/2)⁽ⁿ⁻¹⁾
This is the rule for the nth term of the sequence with the first term 30 and common ratio 1/2.
To find the nth term of the sequence, we simply plug in the value of "n" into the formula. For example, the 5th term of the sequence would be:
a₅ = 30 * (1/2)⁽⁵⁻¹⁾ = 30 * (1/2)⁴ = 30 * 1/16 = 1.875
Therefore, the 5th term of the sequence is 1.875.
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Becky is making fruit salad with strawberries and cherries. She has 1.84 pounds of strawberries and 2.62 pounds of cherries. She mixes the two fruits together and then scoops out 0.25 pounds of fruit salad for each serving. What is the greatest number of 0.25 pound servings Becky can make?
The greatest number of 0.25 pound servings Becky can make is 18.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, Becky has 1.84 pounds of strawberries and 2.62 pounds of cherries.
Now, number of pounds of salads
= 1.84+2.62
= 4.46 pounds
Becky mixes the two fruits together and then scoops out 0.25 pounds of fruit salad for each serving.
So, the number of servings = 4.46/0.25
= 17.84
≈ 18
Therefore, the greatest number of servings is 18.
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Question 2 2 pts Tests for tuberculosis like all other diagnostic tests are not perfect: QFT-G is one of such tests for tuberculosis Suppose that for the population of adults that is taking the test; 5% have tuberculosis The test correctly identifies 74.6% of the time adults with a tuberculosis and correctly identifies those without tuberculosis 76.53% of the time. Suppose that POS stands for the test gives a positive result and S means that the adult really has tuberculosis What is the probability of an adult getting a NEG result and truly NOT having tuberculosis? 0.0373 0.0127 0.2230 0.7270
The probability of an adult getting a NEG result and truly NOT having tuberculosis is 0.7270.
The probability of an adult getting a NEG result and truly NOT having tuberculosis is 0.7270. This can be calculated using Bayes' Theorem, which states that [tex]P(A|B) = (P(B|A) * P(A))/(P(B)).[/tex]
In this problem, P(A) is the probability of having tuberculosis (5%), P(B|A) is the probability of correctly identifying a person with tuberculosis (74.6%), and P(B) is the probability of getting a positive result (the sum of correctly identifying a person with tuberculosis (74.6%) and incorrectly identifying a person without tuberculosis
Therefore, P(A|B) = 0.7270.
The probability of an adult getting a NEG result and truly NOT having tuberculosis is 0.7270.
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If 15−−√×a 15 × a is a rational number, what could be the value of a a ? Explain your reasoning
For the given rational number √15 × a = 15 × a the value of 'a' is equal to 0 or ( 1 / 15 ).
The expression is written as :
√15 × a = 15 × a
The above expression is a rational number :
Squaring both the side of the expression we get,
⇒ 15 × a = ( 15 × a )²
⇒ 15 × a = 225 × a²
Divide by 15 on the both the side of the equation we get,
⇒ a = 15 a²
⇒ 15a² - a = 0
⇒ a( 15a - 1 ) = 0
⇒ a = 0 or 15a - 1 =0
⇒ a = 0 or a = 1 / 15
Therefore, the value of a for the given rational number is equal to
0 or ( 1 / 15 ).
The above question is incomplete , the complete question is:
If √15 × a = 15 × a is a rational number, what could be the value of a ? Explain your reasoning.
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Select the correct answer.
Consider this quadratic equation.
x² + 3 = 4x
Which expression correctly sets up the quadratic formula to solve the equation?
O A.
OB.
O C.
O D.
-(-4) ± √(-4)² - 4(1)(3)
2(1)
-(-4) ± √(-3)² - 4(1)(4)
2(1)
-(-4) ± √4²(1)(3)
2(1)
-4± √√42-4(1)(3)
2(1)
The equation can be solved using the quadratic formula when the following expression is used: [tex]$x=\frac{-(-4)+-\sqrt{(-4)^2-4(1)(3)}}{2(1)}$[/tex]
What is quadratic formula?The quadratic formula in elementary algebra is a formula that gives the solution(s) to a quadratic equation. In addition to the quadratic formula, there are various methods for solving quadratic equations, including factoring (direct factoring, grouping, and the AC technique), completing the square, graphing, and others.
The following general quadratic equation is given:
ax² + bx + c = 0
As a result, a polynomial equation with exponent two is referred to as a quadratic ("square-like") equation. Quadratum is the Latin word for square, and since the area of a square with side length x is given by x2, this is the case.
A quadratic equation's solution(s) can be found using the quadratic formula in elementary algebra. Graphing, factoring (direct factoring, grouping, AC technique), completing the square, and other methods can be used to solve a quadratic equation in addition to the quadratic formula.
The given equation is x² - 4x + 3 = 0
When compared to the quadratic equation's general equation, we get a = 1, b = -4, c = 3.
When the coefficient values for the Sridhar Acharya formula are put in,[tex]$x=\frac{-(-4)+-\sqrt{(-4)^2-4(1)(3)}}{2(1)}$[/tex] which gives Option (A).
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A truck that can carry no more than 6500lb is being used to transport refrigerators and upright pianos. Each refrigerator weighs 300lb and each piano weighs 475lb. Write and graph an inequality to show how many refrigerators and how many pianos the truck could carry. Will 10 refrigerators and 9 pianos overload the truck? Explain.
Answer:
We can write an inequality to represent the weight that the truck can carry:
Weight of Refrigerators + Weight of Pianos <= 6500
Let x be the number of refrigerators and y be the number of pianos. Then we can write:
300x + 475y <= 6500
To determine if 10 refrigerators and 9 pianos would overload the truck, we can substitute the values into the inequality:
300 * 10 + 475 * 9 <= 6500
3000 + 4275 <= 6500
7275 <= 6500
Since 7275 is greater than 6500, this means that 10 refrigerators and 9 pianos would overload the truck.
Graphically, we can plot the points representing the weight of the refrigerators and pianos on the x-y plane, and shade the region below the line representing the inequality to show the combinations of refrigerators and pianos that would not overload the truck. Any point above the line would represent a combination of refrigerators and pianos that would overload the truck.
Hope it helps! : )
Answer:
7275lb
Step-by-step explanation:
Let R be the number of refrigerators and P be the number of pianos. The total weight of the load can be represented as:
Weight = 300R + 475P
The weight must be less than or equal to 6500lb, so we have the inequality:
300R + 475P <= 6500
To graph this inequality, we can first rewrite it in slope-intercept form:
475P <= 6500 - 300R
P <= (6500 - 300R) / 475
Next, we can plot the points (0, 13.68), (22, 0) on the coordinate plane, where (0, 13.68) corresponds to the y-intercept and (22, 0) corresponds to the x-intercept. The graph will be a line that starts at the y-intercept and goes down to the right, passing through (22, 0).
The truck could carry up to 22 refrigerators (when R = 22, P = 0), or up to 13.68 pianos (when R = 0, P = 13.68), or any combination of refrigerators and pianos that results in a weight of less than or equal to 6500lb.
As for the specific case of 10 refrigerators and 9 pianos, the weight can be calculated as:
Weight = 300 * 10 + 475 * 9 = 3000 + 4275 = 7275
This would overload the truck, as the weight of 7275lb is greater than the maximum allowed weight of 6500lb.
Please help, I’ll give brainliest!
assume you have applied to two different universities (let's refer to them as universities a and b) for your graduate work. in the past, 10% of students (with similar credentials as yours) who applied to university a were accepted, while university b accepted 50% of the applicants. assume events are independent of each other. a. what is the probability that you will be accepted to both universities?
If 10% of students who applied to university a were accepted, while university b accepted 50% of the applicants. The probability of being accepted to both universities is 0.05, or 5%.
The probability of being accepted at University A is 10%, which means the probability of not being accepted at University A is 90% (or 0.9). The probability of being accepted at University B is 50%, which means the probability of not being accepted at University B is 50% (or 0.5).
Since the events of being accepted at each university are independent of each other, we can use the multiplication rule of probability to find the probability of being accepted at both universities.
P(A and B) = P(A) x P(B)
where P(A and B) represents the probability of being accepted at both universities, P(A) represents the probability of being accepted at University A, and P(B) represents the probability of being accepted at University B.
Plugging in the values we have:
P(A and B) = 0.1 x 0.5 = 0.05
Therefore, the probability of being accepted to both universities is 0.05, or 5%. This means that there is a very low chance of being accepted at both universities, given the acceptance rates provided.
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If you borrow $1,100 for 9 years at an annual interest rate of 4% , what is the total amount of money you will pay back?
Olivia
has 1/8 pound of butter. She needs to divide the butter equally among 4 batches of muffins she is baking. How much butter is used in each batch of muffins?
If she needs to divide the butter equally then quantity of butter that should be in 4 batches each is 1/32 pond.
According to the question:
Olivia has 1/8 pound of butter. She needs to divide the butter equally among 4 batches of muffins she is baking.
Quantity of butter = 1/8
Number of batches = 4
To find how much butter is used in each batch of muffins, we just have to divide 1/8 pond of butter to 4.
If she needs to divide the butter equally then quantity of butter that should be in 4 batches each = 1/8 ÷ 4 = 1/32 pond
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natasha wants to average at least 90% in math class. her test scores so far are 94%, 89%, 88%, 92%, and 85%. what score does she need to earn on her next test to reach her goal? show your work.
Hey there! Johnny Sins always here to help,
To find out what score Natasha needs to earn on her next test, we can use the following formula:
Average = (sum of all scores) / number of scores
Let's call the score Natasha needs to earn on her next test "x".
Her average so far is:
Average = (94 + 89 + 88 + 92 + 85) / 5 = 90
Her average after her next test will be:
Average = (94 + 89 + 88 + 92 + 85 + x) / 6
Now, we need to set this equal to 90% and solve for x:
90 = (94 + 89 + 88 + 92 + 85 + x) / 6
90 * 6 = (94 + 89 + 88 + 92 + 85 + x)
540 = (94 + 89 + 88 + 92 + 85 + x)
x = 540 - (94 + 89 + 88 + 92 + 85)
x = 540 - 448
x = 92
So, Natasha needs to earn a 92% on her next test to average at least 90%.
_________________________________________________________
No problem for the answer, be sure o give a 5 stars and thanks,
Johnny Sins
What is the total number of digits used to number 1200 pages?
Answer:
The correct answer would be 3693
Step-by-step explanation:
9 + 180 + 2,700 + 804
3693
1200 pages were numbered using a total of 3693 digits.
What is total number?The word "total" refers to the addition of numbers or the destruction of something, and a total is a whole or complete sum. In mathematics, adding two or more numbers yields the sum. When you multiply 8 by 8, you get 16.the total of the acquisition's purchase price plus all future expenses that will be spent, including those for installation, consumables, breakdown, maintenance, and disposal. The sum is the outcome or conclusion of adding two or more numbers or phrases. As a result, the sum is a means of assembling objects. In other terms, the process of adding two or more numbers together to create a new result or total is known as the sum.Total digits equal = the digits in the 1 - digit page numbers + the 2 digit page numbers - digit page numbers + 3 digit page numbers - digit page numbers.
Then simplify,
9 + 180 + 2,700 + 804
= 3693
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Consider the system of equations -2x + 3y = -5 and 3x - 4y = 6.
-Describe two different ways to solve the system by elimination. Select ALL that apply.
A) Multiply the first equation by 4, the second equation by 3, and subtract to eliminate y,
B) Multiply the first equation by 3, the second equation by 2, and subtract to eliminate x
c) Multiply the first equation by 3, the second equation by 2, and add to eliminate x.
D) Multiply the first equation by 3, the second equation by -2, and add to eliminate x
E) Multiply the first equation by 4, the second equation by 3, and add to eliminate y
F) Multiply the first equation by -4, the second equation by 3, and add to eliminate y
(Write below which of the letter answer(s) it is)
Two ways of solving the system of equations are:
c) Multiply the first equation by 3, the second equation by 2, and add to eliminate x.E) Multiply the first equation by 4, the second equation by 3, and add to eliminate yWhich two ways can be used to solve the system of equations?Here we want to identify two ways of solving the system of equations:
-2x + 3y = -5
3x - 4y = 6
One way is using the elimination method, then the option E is true, if we multiply the first equation by 4 and the second by 3 and then we add the two equations, the variable y will be eliminated and we could solve the equation for x.
We also could eliminate the variable x, to do so, we need to multiply the first equation by 3 and the second by 2, and add the two equations.
Then option C is also true.
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Colton's gross pay is $1421.50 and his net pay is $973.48.
What percent of his gross pay is take-home pay?
31.5%
44.8%
46%
68.5%
68.5% of Colton's gross pay is take-home pay. To find the percentage of Colton's gross pay that is take-home pay, we need to divide his net pay by his gross pay and then multiply by 100 to convert the resulting decimal to a percentage.
To find the percentage of Colton's gross pay that is take-home pay, we need to divide his net pay by his gross pay and multiply the resulting decimal by 100 to express it as a percentage. Colton's gross pay is $1421.50 and his net pay is $973.48. Dividing the net pay by the gross pay gives a result of 0.685, or 68.5% when converted to a percentage. This means that 68.5% of Colton's gross pay is take-home pay, or the amount of money that he receives after deductions are made. Therefore, Colton's take-home pay is $973.48, which is 68.5% of his gross pay.
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A room is 11 ft by 20 ft. It needs to be painted. The ceiling is 8 ft above the floor. There are two windows in the room, each one is 3 ft by 4 ft. The door is 2.5 ft by 6.5 ft.
Part 2
a) Find the area of the walls and ceiling to be painted.
b) One gallon of paint covers 71.41 sq ft. How many gallons are needed to paint the room?
c) At $18.32 a gallon, what is the cost to paint the room?
The required answers are,
a) 675.75 [tex]ft^2[/tex]
b) 9.46 gallons or we can say that 10 gallons needed.
c) $183.2
What is Area:The amount of unit squares that cover a closed figure's surface is its area. Area is measured in square units like cm² and m². Area of a shape is a two dimensional quantity. The term “area” refers to the space inside the boundary or perimeter of a closed shape.
Now in the given question,
Area of Walls:
[tex]A(walls)=2(11*8)+2(20*8)\\A(walls)=2(88)+2(160)\\A(walls)=176+320\\A(walls)=496 ft^2[/tex]
Area of 2 windows:
[tex]A(windows)=2(3*4)\\A(windows)=2*12\\A(windows)=24 ft^2[/tex]
Area of door:
[tex]A(door)=2.5*6.5\\A(door)=16.25 ft^2[/tex]
Area of walls to be painted:
[tex]=A(walls)-A(windows)-A(door)\\=496-24-16.25\\=455.75ft^2[/tex]
Area of ceiling:
[tex]A(ceiling)=11*20\\A(ceiling)=220ft^2[/tex]
(a) Now total area to be painted:
A(walls to be painted)+ A(ceiling)=A(total)
[tex]A(total)=455.75 ft^2+220ft^2\\A(total)=675.75 ft^2[/tex]
(b) Number of Gallons:
coverage=71.41 ft^2 /gallon
675.75 ft^2/71.41 ft^/gal=gallons needed
9.46 gal= 10 gallons needed(approx)
(c) Cost of Paint:
You would need to buy 10 gallons at $18.32/gallon to have sufficient paint
cost=10 gallons x $18.32/gallon
=$183.2
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Point B is located at (-4, -6) on the coordinate plane. Point B is reflected over the x-axis to create point B'. Point B' is then reflected over the y-axis to create point
B". What ordered pair describes the location of B"?
Answer:
The ordered pair for point B after it has been reflected over both the x and y-axis is (4, 6).
This is due to the rule for reflecting over the x-axis, which is to negate the value of the y-coordinate of each point, but leave the x-value the same. This means that after reflecting point B over the x-axis, it's new coordinates would be (-4, 6).
The rule for reflecting over the y-axis is to negate the value of the x-coordinate of each point, but leave the y-value the same. This means that after reflecting point B' over the y-axis, it's new coordinates would be (4, 6).
Let’s see who gets this right..
Travel agents were designing a marketing program to promote tourism in Canada. To determine the target audience for their program, the travel agents surveyed people across two different age groups about whether they have been to Canada in the past six months. The table below shows the results of the survey.
Answer: 63%
Step-by-step explanation:
22 divided by 35 times 100
if the first one to arrive will wait only 20 min before leaving to eat elsewhere, what is the probability that they have dinner at the health-food restaurant? [hint: the event of interest is a
The probability that they have dinner at the health food restaurant is 0.643.
To calculate the probability that the first one to arrive has dinner at the health-food restaurant given that they will wait only 20 minutes before leaving to eat elsewhere, we need to use conditional probability.
Let A be the event that the first one to arrive has dinner at the health-food restaurant, and let B be the event that the first one to arrive waits only 20 minutes before leaving to eat elsewhere.
We want to find P(A|B), the probability that A occurs given that B occurs.
We know that P(A) = 0.3, the probability that the first one to arrive has dinner at the health-food restaurant. We also know that P(B|A) = 0.6, the probability that the first one to arrive waits only 20 minutes before leaving to eat elsewhere given that they have dinner at the health-food restaurant.
To calculate P(B), the probability that the first one to arrive waits only 20 minutes before leaving to eat elsewhere, we need to use the law of total probability:
P(B) = P(B|A) x P(A) + P(B|A') x P(A')
where A' is the complement of A, i.e., the event that the first one to arrive does not have dinner at the health-food restaurant. We know that P(A') = 1 - P(A) = 1 - 0.3 = 0.7, and we are given that P(B|A') = 0.1, the probability that the first one to arrive waits only 20 minutes before leaving to eat elsewhere given that they do not have dinner at the health-food restaurant.
Therefore, we can calculate P(B) as:
P(B) = P(B|A) x P(A) + P(B|A') x P(A')
= 0.6 x 0.3 + 0.1 x 0.7
= 0.21 + 0.07
= 0.28
Finally, we can calculate P(A|B) using Bayes' theorem:
P(A|B) = P(B|A) x P(A) / P(B)
= 0.6 x 0.3 / 0.28
= 0.643
Therefore, the probability that the first one to arrive has dinner at the health-food restaurant given that they will wait only 20 minutes before leaving to eat elsewhere is approximately 0.643 or 64.3%.
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CAN SOMEONE HELP ASAP! ITS FOR HOMEWORK AND I DONT KNOW HOW TO DO ANYTHING !!!
The missing angles are
A. = 130 degrees
B. = 55 degrees
C. = 145 degrees
D. = 73 degrees
E. = 43 degrees
F. = 23 degrees
G. = 61 degrees
H. = 90 degrees
I. = 50 degrees
J. = 27 degrees
K. = 25 degrees
How to find the valuesAssuming the missing angle in each case is x
A. Angle on a straight line = 180 degree
x + 50 = 180
x = 130 degrees
B. Angle at a point = 360 degrees
209 + 96 + x = 360
x = 360 - 96 - 209
= 55 degrees
C. Angle on a straight line = 180 degree
= 145 degrees
D. Vertical angles are equal, using vertical angle theorem
= 73 degrees
E. vertical angle theorem
= 43 degrees
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jess bought 3.2 yards of fabric and paid 24.96. dollors how much did she pay per yard?
She paid $0.1282051282 per yard - $0.13 ( rounded ).
Sage and Tom started the month with the same number of talk minutes on their cell phones. Sage talked for 7 minutes with her dad. Tom talked for 4 minutes with a friend and 3 more minutes with his mom. Do Sage and Tom have the same number of talk minutes left on their cell phone plans?
Question 1
Yes, Sage and Tom have the same number of talk minutes left in their cell phones. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
The term "arithmetic operations" refers to the four basic mathematical operations that can be used to express any real number. Multiplication, division, addition, and subtraction are the four operations.
We are given that Sage and Tom both started the month with the same number of talk minutes on their cell phones.
So, let 'x' be the number of talk minutes on their cell phones.
Sage talked for 7 minutes with her dad.
So, talk minutes left in Sage's phone = x-7
Tom talked for 4 minutes with a friend and 3 more minutes with his mom.
So, talk minutes left in Tom's phone = x - (4 +3) = x -7
Hence, Sage and Tom have the same number of talk minutes left in their cell phones.
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I need help with this
The unknown angles are as follows:
m∠1 = 117°
m∠3 = 68°
m∠4 = 22°
m∠5 = 90°
How to find angle relationship?When lines intersect angle relationships are formed such as linear angles, vertically opposite angles etc.
Therefore,
m∠1 = 180 - 63(sum of angles on a straight line)
m∠1 = 117 degrees
Hence,
m∠3 = 68 degrees(vertical angles)
Vertically opposite angles are congruent.
Hence,
m∠4 = 90 - 68
m∠4 = 22 degrees
Hence,
m∠5 = 90 degrees(right angle)
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Calculate the problem A sum of money was shared between Mario, Giana and Allan in the 2:3:7. If Allan received $640 more than Giana, find the total sum of money shared
The total amount of money Mario, Giana, and Allan split was $2160. Giana received $640 less than Allan did.
Let x represent the sum of money Mario got.
Giana got three times
Allan got seven times
Total: 2x, 3x, 7x, or 12x.
Allan received $640 more than Giana, therefore
7x = 640 + 3x
4x = 640
x = 160
Total amount split is 12x, or 12 * 160, or $2160.
The total amount of money Mario, Giana, and Allan split was $2160. To determine the overall amount, we must first determine how much money each person received. We know that Giana received three times as much as Mario did, while Allan received seven times as much. So, using 2x, 3x, and 7x, respectively, where x is the amount of money Mario received, we can express how much each person earned.
We may draw up an equation to determine how much money Mario received by taking into account the fact that Allan received $640 more than Giana. It goes like this: 7x = 640 + 3x. x = 160 is the result of solving this equation. Mario thus received $160 whereas Giana received $480 after multiplying 3x by 3 * 160. Allan received $1120 since he was paid $640 more than Giana (7x = 7 * 160). Mario, Giana, and Allan divided the total amount of money as follows: 2x + 3x + 7x = 12x = 12 * 160 = $2160.
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there are three coins in a box. one is a two-headed coin, another is a fair coin, and the third is a biased coin that comes up heads 80% of the time. (a) when one of these coins were selected at random and flipped, what is the probability that it shows heads? (1 po
The probability of the selected coin showing heads is 0.77, or 77%.
Probability is the measure of the likelihood of an event occurring. In this scenario, we have three coins in a box, each with different properties.
To calculate the probability of an event occurring, we need to divide the number of favorable outcomes by the total number of possible outcomes. In this case, there are three possible coins we could select, each with a different probability of showing heads.
Now, we need to determine the total number of possible outcomes, which is simply the number of coins we have, which is three.
Next, we need to determine the number of favorable outcomes. For Coin 1, the probability of showing heads is 1 (since it has two heads). For Coin 2, the probability of showing heads is 0.5 (since it is a fair coin with equal probability of heads and tails). For Coin 3, the probability of showing heads is 0.8.
To calculate the probability of showing heads when we randomly select one of these coins, we need to weigh the probabilities of each coin being selected with their corresponding probabilities of showing heads.
Let's say that the probability of selecting each coin is equal (since we have no information to suggest otherwise). Then, the probability of selecting Coin 1 is 1/3, the probability of selecting Coin 2 is 1/3, and the probability of selecting Coin 3 is 1/3.
To calculate the overall probability of showing heads, we can use the following formula:
P(heads) = (P(Coin 1) * P(heads on Coin 1)) + (P(Coin 2) * P(heads on Coin 2)) + (P(Coin 3) * P(heads on Coin 3))
= (1/3 * 1) + (1/3 * 0.5) + (1/3 * 0.8)
= 0.77
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A large data set includes samples of body temperatures. Analyzing one sample of body temperatures results in n=107, x=98.19°F, and s=0.624°F. It is
commonly believed that humans have a mean body temperature of 98.6°F. If the analysis is repeated with a different sample and it is found that for 100
randomly generated samples, 38 of these generated samples have a mean that is as extreme as the mean of the actual sample, what should be concluded
about the assumed mean of 98.6°F? (Assume that an event is significant if it has a probability of 0.05 or less.)
Since 38 of the 100 samples have means that are as much as the sample mean, then that sample mean
strong evidence against the assumed mean of 98.6°F. It appears the population mean
▼98.6°F.
so there
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The side length of a square is( 2/3g+1) cm. Use this information to complete parts (a) and (b)
The perimeter of a square with length of a side given as 2/3g + 1 cm is 8/3g + 1 cm.
Let's call the length of a side of the square "s". According to the information given, s = 2/3g + 1 (in cm).
The perimeter of a square is equal to the sum of the lengths of all four sides, so we can write an expression to represent the perimeter as follows:
P = 4s
Substituting the expression for s from above, we get:
P = 4(2/3g + 1)
So, the expression for the perimeter of the square in terms of g is:
P = 4(2/3g + 1)
Therefore, P = 8/3g + 1.
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Complete question: the length of a square is( 2/3g+1)cm use this information to write an expression to represent the perimeter of the square.
